Menu

Efficient spherical harmonic shading for separable BRDF

Pierre Mézières, Mathias Paulin
ACM Digital Library, SIGGRAPH Asia 2021 Technical Communications, SA’21
⟨hal-03358603⟩

Abstract: Spherical Harmonics (SH) are commonly and widely used in computer graphics in order to speed up the evaluation of the rendering equation. With separable BRDF, the diffuse and specular contributions are traditionally computed separately. Our first contribution is to demonstrate that there is a simple relationship between both computations, but one-way, i.e. from specular to diffuse. We show how to deduce the diffuse contribution from the specular contribution, using a single multiplication. This replaces the use of tens of multiplications for some cases up to complex rotations for other cases. Our second contribution is an efficient way to compute the SH product between an arbitrary function and a clamped cosine, much less expensive than the traditional SH triple product.

Computing per-pixel shading using Spherical Harmonics (SH) is a costly task that requires to compute a triple SH product when evaluating specular contribution. In this work we derive a new formulation of this product for separable BRDFs. Our approach reduces computation timings by two orders of magnitude and improves the quality of the final image (as measured by RMSE). Top: images obtained with our approach using 9 SH bands. Bottom: Reference images generated by sampling 10.000 rays for each light.

Acknowledgment: This project was partially funded by the CaLiTrOp project from French National Research Agency (ANR-16-CE33-0026).
Sponza and Gallery taken from the McGuire Computer Graphics Archive. Living room created by Wig42. Elephant taken from Sumner and Popovic.

Article
Supp. mat.